North Carolina Republican Party Chairman Tom Fetzer said there have been reports that a voter trying to cast a "straight ticket" for the Republicans actually registers as a straight ticket Democrat vote.
The complaint filed in federal court accuses election officials of failing to take action to ensure votes are accurately counted.
Election officials have said there have only been a few isolated problems with voting machines and that officials were able to quickly fix the problems.
Republican Party officials say they have heard problems in a number of counties. They are demanding that election officials provide notice to all voters about problems, preserve all data and track all complaints.